Abstract
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation.
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Communicated by P.-L. Lions
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Mellet, A., Mischler, S. & Mouhot, C. Fractional Diffusion Limit for Collisional Kinetic Equations. Arch Rational Mech Anal 199, 493–525 (2011). https://doi.org/10.1007/s00205-010-0354-2
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DOI: https://doi.org/10.1007/s00205-010-0354-2